S. Klepper, Economics 73-100, Fall 2011

# Solution to Mini-test 1

If each unit of food requires one unit of labor and the country has 500 units of labor, then it can produce a maximum of 500 units of food.  Regarding shelter, the first 200 units of shelter require 100 units of labor to produce.  The next 200 require 200 units of labor, which leaves 200 units of labor for all subsequent units of shelter. Each of these subsequent units requires two units of labor, so that 100 additional units of shelter can be produced.  Consequently, in total 500 units of shelter can be produced.

Suppose the country devotes all its labor to shelter, thus producing 500 units of shelter and 0 units of food.  To produce one unit of food, one unit of labor is required.  If one unit of labor is taken from shelter production, shelter production is initially reduced by one-half of a unit.  This will continue until 200 units of food are produced, using 200 units of labor.  Thus, the opportunity cost of each of the first 200 units of food is equal to one-half of a unit of shelter.  When 200 units of food are produced using 200 units of labor, 300 units of labor will be left to produce shelter.  As one additional unit of labor is transferred to food to increase food production by one unit, shelter production will then fall by one unit. This will continue to hold for the production of the next 200 units of food.  Thus, the opportunity cost of each of the next 200 units of food above 200 is one unit of shelter.  After 400 units of food are produced, each additional unit of food will again require one unit of labor, but the transfer of this one unit of labor from shelter will reduce the number of units of shelter produced by two units.  Therefore, the opportunity cost of each unit of food doubles after 200 units of food are produced and then doubles again after 400 units of food are produced.  Regarding shelter, the opportunity cost of each of the first 200 units is one-half unit of food since each of the first 200 units of shelter requires one-half unit of labor.  The next 200 units of shelter each require one unit of labor, hence the opportunity cost of each of the next 200 units of shelter is one unit of food.  Further units of shelter each require two units of labor, hence the opportunity cost of each of these units of shelter is two units of food. Therefore, the opportunity cost of shelter doubles after 200 units of shelter are produced and then doubles again after 400 units of shelter are produced.

Based on this description, the answers to the individual questions are:

_____1. True

_____2. False

_____3. True

_____4. False

_____5. True